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Sep 18, 2013
09/13

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Yoh Tanimoto

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We review our recent construction of operator-algebraic quantum field models with a weak localization property. Chiral components of two-dimensional conformal fields and certain endomorphisms of their observable algebras play a crucial role. In one case, this construction leads to a family of strictly local (Haag-Kastler) nets.

Source: http://arxiv.org/abs/1209.1370v2

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Jul 20, 2013
07/13

by
Yoh Tanimoto

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In higher dimensional quantum field theory, irreducible representations of the Poincare group are associated with particles. Their counterpart in two-dimensional massless models are "waves" introduced by Buchholz. In this paper we show that waves do not interact in two-dimensional Moebius covariant theories and in- and out-asymptotic fields coincide. We identify the set of the collision states of waves with the subspace generated by the chiral components of the Moebius covariant net...

Source: http://arxiv.org/abs/1107.2662v2

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Jun 29, 2018
06/18

by
Yoh Tanimoto

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We consider scalar two-dimensional quantum field theories with the factorizing S-matrix which has poles in the physical strip. In our previous work, we introduced the bound state operators and constructed candidate operators for observables in wedges. Under some additional assumptions on the S-matrix, we show that, in order to obtain their strong commutativity, it is enough to prove the essential self-adjointness of the sum of the left and right bound state operators. This essential...

Topics: High Energy Physics - Theory, Mathematical Physics, Operator Algebras, Mathematics

Source: http://arxiv.org/abs/1602.04696

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Jun 28, 2018
06/18

by
Yoh Tanimoto

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We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class of analytic functions. For functions of a particular form, we point out the existence of a self-adjoint extension which is unitarily equivalent to the analytic-continuation operation. They appear in integrable quantum field theories as the one-particle...

Topics: Functional Analysis, Mathematical Physics, Mathematics, Complex Variables

Source: http://arxiv.org/abs/1508.06402

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Sep 23, 2013
09/13

by
Yoh Tanimoto

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We consider cones in a Hilbert space associated to two von Neumann algebras and determine when one algebra is included in the other. If a cone is assocated to a von Neumann algebra, the Jordan structure is naturally recovered from it and we can characterize projections of the given von Neumann algebra with the structure in some special situations.

Source: http://arxiv.org/abs/0801.4259v2

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Jul 20, 2013
07/13

by
Yoh Tanimoto

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A convenient framework to treat massless two-dimensional scattering theories has been established by Buchholz. In this framework, we show that the asymptotic algebra and the scattering matrix completely characterize the given theory under asymptotic completeness and standard assumptions. Then we obtain several families of interacting wedge-local nets by a purely von Neumann algebraic procedure. One particular case of them coincides with the deformation of chiral CFT by Buchholz-Lechner-Summers....

Source: http://arxiv.org/abs/1107.2629v2

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Sep 21, 2013
09/13

by
Yoh Tanimoto

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The group Diff(S^1) of the orientation preserving diffeomorphisms of the circle S^1 plays an important role in conformal field theory. We consider a subgroup B_0 of Diff(S^1) whose elements stabilize "the point of infinity". This subgroup is of interest for the actual physical theory living on the punctured circle, or the real line. We investigate the unique central extension K of the Lie algebra of that group. We determine the first and second cohomologies, its ideal structure and...

Source: http://arxiv.org/abs/0905.0875v3

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Jul 19, 2013
07/13

by
Yoh Tanimoto

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Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S^1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg.

Source: http://arxiv.org/abs/1005.0270v2

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Sep 21, 2013
09/13

by
Yoh Tanimoto

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We present a procedure to construct families of local, massive and interacting Haag-Kastler nets on the two-dimensional spacetime through an operator-algebraic method. An existence proof of local observable is given without relying on modular nuclearity. By a similar technique, another family of wedge-local nets is constructed using certain endomorphisms of conformal nets recently studied by Longo and Witten.

Source: http://arxiv.org/abs/1301.6090v1

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0.0

Jun 29, 2018
06/18

by
Roberto Longo; Yoh Tanimoto

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We consider KMS states on a local conformal net on the unit circle with respect to rotations. We prove that, if the conformal net is of type I, namely if it admits only type I DHR representations, then the extremal KMS states are the Gibbs states in an irreducible representation. Completely rational nets, the U(1)-current net, the Virasoro nets and their finite tensor products are shown to be of type I. In the completely rational case, we also give a direct proof that all factorial KMS states...

Topics: High Energy Physics - Theory, Mathematical Physics, Operator Algebras, Mathematics

Source: http://arxiv.org/abs/1608.08903

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Sep 23, 2013
09/13

by
Wojciech Dybalski; Yoh Tanimoto

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We formulate a new concept of asymptotic completeness for two-dimensional massless quantum field theories in the spirit of the theory of particle weights. We show that this concept is more general than the standard particle interpretation based on Buchholz' scattering theory of waves. In particular, it holds in any chiral conformal field theory in an irreducible product representation and in any completely rational conformal field theory. This class contains theories of infraparticles to which...

Source: http://arxiv.org/abs/1112.4102v2

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Jun 29, 2018
06/18

by
Daniela Cadamuro; Yoh Tanimoto

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In the bootstrap approach to integrable quantum field theories in the (1+1)-dimensional Minkowski space, one conjectures the two-particle S-matrix and tries to study local observables. The massless sine-Gordon model is conjectured to be equivalent to the Thirring model, and its breather-breather S-matrix components (where the first breather corresponds to the scalar field of the sine-Gordon model) are closed under fusion. Yet, the residues of the poles in this breather-breather S-matrix have...

Topics: High Energy Physics - Theory, Mathematical Physics, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1612.02073

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3.0

Jun 26, 2018
06/18

by
Daniela Cadamuro; Yoh Tanimoto

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Recently, large families of two-dimensional quantum field theories with factorizing S-matrices have been constructed by the operator-algebraic methods, by first showing the existence of observables localized in wedge-shaped regions. However, these constructions have been limited to the class of S-matrices whose components are analytic in rapidity in the physical strip. In this work, we construct candidates for observables in wedges for scalar factorizing S-matrices with poles in the physical...

Topics: High Energy Physics - Theory, Mathematics, Operator Algebras, Mathematical Physics

Source: http://arxiv.org/abs/1502.01313

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Sep 23, 2013
09/13

by
Marcel Bischoff; Yoh Tanimoto

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In the first part, we have constructed several families of interacting wedge-local nets of von Neumann algebras. In particular, there has been discovered a family of models based on the endomorphisms of the U(1)-current algebra of Longo-Witten. In this second part, we further investigate endomorphisms and interacting models. The key ingredient is the free massless fermionic net, which contains the U(1)-current net as the fixed point subnet with respect to the U(1) gauge action. Through the...

Source: http://arxiv.org/abs/1111.1671v2

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Sep 23, 2013
09/13

by
Wojciech Dybalski; Yoh Tanimoto

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This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges. It is shown that the scattering theory for waves in two dimensions, due to...

Source: http://arxiv.org/abs/1006.5430v2

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0.0

Jun 29, 2018
06/18

by
Daniela Cadamuro; Yoh Tanimoto

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We construct candidates for observables in wedge-shaped regions for a class of 1+1-dimensional integrable quantum field theories with bound states whose S-matrix is diagonal, by extending our previous methods for scalar S-matrices. Examples include the Z(N)-Ising models, the A_N-affine Toda field theories and some S-matrices with CDD factors. We show that these candidate operators which are associated with elementary particles commute weakly on a dense domain. For the models with two species of...

Topics: High Energy Physics - Theory, Mathematical Physics, Operator Algebras, Mathematics

Source: http://arxiv.org/abs/1601.07092

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0.0

Jun 30, 2018
06/18

by
Yul Otani; Yoh Tanimoto

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We consider the entanglement entropy for a spacetime region and its spacelike complement in the framework of algebraic quantum field theory. For a M\"obius covariant local net satisfying a certain nuclearity property, we consider the von Neumann entropy for type I factors between local algebras and introduce an entropic quantity. Then we implement a cutoff on this quantity with respect to the conformal Hamiltonian and show that it remains finite as the distance of two intervals tends to...

Topics: High Energy Physics - Theory, Operator Algebras, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1701.01186

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Sep 22, 2013
09/13

by
Wojciech Dybalski; Yoh Tanimoto

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Particle aspects of two-dimensional conformal field theories are investigated, using methods from algebraic quantum field theory. The results include asymptotic completeness in terms of (counterparts of) Wigner particles in any vacuum representation and the existence of (counterparts of) infraparticles in any charged irreducible product representation of a given chiral conformal field theory. Moreover, an interesting interplay between the infraparticle's direction of motion and the...

Source: http://arxiv.org/abs/1101.5700v2

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Sep 18, 2013
09/13

by
Gandalf Lechner; Jan Schlemmer; Yoh Tanimoto

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Two recent deformation schemes for quantum field theories on the two-dimensional Minkowski space, making use of deformed field operators and Longo-Witten endomorphisms, respectively, are shown to be equivalent.

Source: http://arxiv.org/abs/1209.2547v3

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Jun 29, 2018
06/18

by
Vincenzo Morinelli; Yoh Tanimoto; Mihály Weiner

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We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e. diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, M\"obius covariance does not imply the split property. On the other hand, here we also provide an example of a local conformal net living on the two-dimensional Minkowski space, which...

Topics: High Energy Physics - Theory, Mathematical Physics, Operator Algebras, Mathematics

Source: http://arxiv.org/abs/1609.02196

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Sep 23, 2013
09/13

by
Paolo Camassa; Roberto Longo; Yoh Tanimoto; Mihaly Weiner

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We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on the real line. In the first part we have proved the uniqueness of KMS state on every completely rational net. In this second part, we exhibit several (non-rational) conformal nets which admit continuously many primary KMS states. We give a complete classification of the KMS states on the U(1)-current net and on the Virasoro net Vir_1 with the...

Source: http://arxiv.org/abs/1109.2064v2

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Sep 22, 2013
09/13

by
Paolo Camassa; Roberto Longo; Yoh Tanimoto; Mihály Weiner

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We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on R. In this first part, we focus on completely rational net A. Our main result here states that, if A is completely rational, there exists exactly one locally normal KMS state \phi. Moreover, \phi is canonically constructed by a geometric procedure. A crucial r\^ole is played by the analysis of the "thermal completion net" associated with a locally normal...

Source: http://arxiv.org/abs/1101.2865v2